With a vital win in the Georgia primary Tuesday, Republican presidential candidate Newt Gingrich quickly looked ahead to the next round of contests, promising yet another comeback for what he called "the power of ideas."

The victory, the only one besides the Jan. 21 South Carolina primary, hardly brings the former House speaker within striking distance of former Massachusetts Gov. Mitt Romney or former Pennsylvania Sen. Rick Santorum, who racked up more states in Tuesday's 10-state gauntlet.

But it keeps Gingrich's roller-coaster campaign going, with a round of contests including Southern primaries only days away.

"Tomorrow will bring another chapter in the race for the nomination, but it's more than a chapter in the race for the nomination," Gingrich told cheering supporters at a suburban Atlanta hotel. "It's a chapter in a fight for the soul of the Republican Party. It's a chapter in the fight for the very nature of America. It's a chapter defining who we are as a people."

Gingrich, who regained some of his footing in Georgia after a six-week winless stretch, pledged to continue campaigning and planned to fly Wednesday morning to Alabama, and campaign Thursday in Mississippi. Both hold primaries on March 13.

"I want you to know in the morning we are going on to Alabama. We're going on to Mississippi. We're going on to Kansas, and that's just this week," he said.

Gingrich had already campaigned in Alabama Tuesday before the polls closed in neighboring Georgia. The trip to Huntsville and speech at the U.S. Space and Rocket Center there was aimed partly at seizing on the expected Georgia win, but also projecting past Super Tuesday.

He admitted that he would have had little credibility to proceed, had he not won the state where voters had elected him to Congress for 20 years.

Instead, he accepted victory in the same hotel where in 1994 he learned that Republicans had taken control of the U.S. House for the first time in 40 years, guaranteeing him the speakership that made him a national figure.

"And, you know, for that entire campaign, all of the elites thought we were crazy," he said, referring to the campaign's signature Contract With America platform.

Gingrich has billed himself as the ideas candidate in the race against Romney, Santorum and Texas Congressman Ron Paul. Romney and Santorum have at times mocked Gingrich, who has touted far-flung ideas, such as lighting U.S. highways with mirrors in space.

But the former college professor doubled down on his belief that the U.S. can lead space exploration again by visiting the U.S. Space and Rocket Center in Huntsville, Ala., Tuesday.

"This is the launching pad for the next phase of excitement and invention," Gingrich said in the center's museum, in the shadow of a model of a Saturn rocket. He was referring to the space program, but may as well have been referring to his campaign.

Gingrich's campaign has spiraled downward three times in the past 10 months, only to rise twice, notably before his comeback win in the Jan. 21 South Carolina primary, his lone victory in the campaign.

Gingrich was looking to build on his Southern strength, but lost Tennessee to Santorum despite barnstorming the state Monday and introducing a late round of television ads.

Even if the results were mixed, Gingrich returned to a theme that lifted him: Pitting himself squarely against Obama.

"And let me be very clear. I believe that I am the one candidate who has the ability to debate Barack Obama decisively," Gingrich told the audience in Atlanta, prompting cheers.

Gingrich's peaks have come on the heels of standout performances during key debates in the series of 20 held since last May. However, there are no GOP debates scheduled. Still, Gingrich has said he will invite his rivals to debate in Alabama and Mississippi before March 13.

Gingrich also has been helped by four political action committees, including one financed largely by billionaire casino mogul Sheldon Adelson.

Yet Gingrich sought to portray a win in Georgia as a triumph in light of heavy spending on anti-Gingrich attack ads by the pro-Romney political action committee Restore Our Future.